Travelling Wave Solutions for Reaction-diffusion-advection Equations
Author : 裘愉生
Publisher :
Page : 98 pages
File Size : 29,32 MB
Release : 2010
Category :
ISBN :
Author : 裘愉生
Publisher :
Page : 98 pages
File Size : 29,32 MB
Release : 2010
Category :
ISBN :
Author : Brian H. Gilding
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 45,96 MB
Release : 2004-07-23
Category : Mathematics
ISBN : 9783764370718
This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion. Brian worked under the guidance of Bert Peletier at the University of Sussex in Brighton, England, and, later at Delft University of Technology in the Netherlands on extending the earlier mathematics to include nonlinear convection; while Robert worked at Lomonosov State Univer sity in Moscow under the supervision of Anatolii Kalashnikov on generalizing the earlier mathematics to include nonlinear absorption. We first met at a conference held in Rome in 1985. In 1987 we met again in Madrid at the invitation of Ildefonso Diaz, where we were both staying at 'La Residencia'. As providence would have it, the University 'Complutense' closed down during this visit in response to student demonstra tions, and, we were very much left to our own devices. It was natural that we should gravitate to a research topic of common interest. This turned out to be the characterization of the phenomenon of finite speed of propagation for nonlin ear reaction-convection-diffusion equations. Brian had just completed some work on this topic for nonlinear diffusion-convection, while Robert had earlier done the same for nonlinear diffusion-absorption. There was no question but that we bundle our efforts on the general situation.
Author : Hinwa Leung
Publisher :
Page : 176 pages
File Size : 32,82 MB
Release : 1994
Category : Differential equations, Nonlinear
ISBN :
Author : Joshua Rabinowitz
Publisher :
Page : 420 pages
File Size : 19,47 MB
Release : 1994
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ISBN :
Author : Joel Smoller
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 34,36 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461208734
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.
Author : D. Terman
Publisher :
Page : 19 pages
File Size : 22,7 MB
Release : 1983
Category :
ISBN :
A new method for proving the existence of traveling wave solutions for equations is presented. The results describe when, for a given function F, there must exist zero, exactly one, a finite number, or an infinite number of waves which connect two fixed, stable rest points. Author keywords include: Reaction-diffusion equation; Traveling wave solution.
Author : Sven Badke
Publisher :
Page : 0 pages
File Size : 11,98 MB
Release : 2016
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ISBN :
Author : Joaquín Rivera
Publisher :
Page : 164 pages
File Size : 35,10 MB
Release : 2007
Category : Influenza
ISBN :
Author : Stephen Buonincontri
Publisher :
Page : 218 pages
File Size : 17,6 MB
Release : 1989
Category : Reaction-diffusion equations
ISBN :
Author : Aizik I.. Volpert
Publisher : American Mathematical Soc.
Page : 448 pages
File Size : 40,40 MB
Release : 2000
Category : Mathematics
ISBN : 9780821811436
The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. The main part of the book contains original approaches developed by the authors. Among these are a description of the long-term behavior of the solutions by systems of waves; construction of rotations of vector fields for noncompact operators describing wave solutions; a proof of the existence of waves by the Leray-Schauder method; local, global, and nonlinear stability analyses for some classes of systems; and a determination of the wave velocity by the minimax method and the method of successive approximations.The authors show that wide classes of reaction-diffusion systems can be reduced to so-called monotone and locally monotone systems. This fundamental result allows them to apply the theory to combustion and chemical kinetics. With introductory material accessible to nonmathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.